Finite Group Databasebeta

← C22×C13×#585 #15749439

Subgroups — C22×C13×#585 #15749439

Order 3328.

60366 conjugacy classes of subgroups.

The subgroup lattice has 126 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#585C2196yesmaximal, direct product factor
2C22×C13×2−1+4C216yesmaximal, complemented
3C22×C13×H(5,𝔽2)C2110yesmaximal, complemented
4C23×C13×#41C2115yesmaximal, complemented
5C13×#585C2211024yesdirect product factor
6C2×C13×2−1+4C221288yescomplemented
7C2×C13×H(5,𝔽2)C221480yescomplemented
8C22×C13×#41C22120yescomplemented
9C22×C13×#41C22160yescomplemented
10C22×C13×#41C221720yescomplemented
11C23×Q8×C13C22115yescomplemented
12C23×D4×C13C22145yescomplemented
13C24×C4×C13C22115yescomplemented
14C25×C13C23115yes—
15C13×2−1+4C2311536yescomplemented
16C13×H(5,𝔽2)C2312560yescomplemented
17C2×C13×#41C231480yescomplemented
18C2×C13×#41C2311440yescomplemented
19C2×C13×#41C2313840yescomplemented
20C22×Q8×C13C23120yes—
21C22×Q8×C13C231360yescomplemented
22C22×D4×C13C23160yes—
23C22×D4×C13C2311080yescomplemented
24C23×C4×C13C23145yes—
25C23×C4×C13C23115yes—
26C23×C4×C13C231360yescomplemented
27C22×#585C1311yesmaximal, characteristic, direct product factor, Sylow
28C24×C13—460no—
29C24×C13C24115yes—
30C24×C13C241180yes—
31C13×#41C2411280yescomplemented
32C13×#41C2413840yescomplemented
33C2×Q8×C13C241240yes—
34C2×Q8×C13C241960yescomplemented
35C2×D4×C13C241720yes—
36C2×D4×C13C2412880yescomplemented
37C22×C4×C13C24115yes—
38C22×C4×C13C241180yes—
39C22×C4×C13C241540yes—
40C22×C4×C13C2411yescharacteristic
41C22×C4×C13C241960yescomplemented
42C2×#585C2×C13196yesdirect product factor
43C22×2−1+4C2×C1316yescomplemented
44C22×H(5,𝔽2)C2×C13110yescomplemented
45C23×#41C2×C13115yescomplemented
46C23×C13—260no—
47C23×C13—4360no—
48C23×C13C25190yes—
49C23×C13C251240yes—
50C23×C13C2511yescharacteristic
51Q8×C13C251320yes—
52D4×C13C251960yes—
53C2×C4×C13C2516yes—
54C2×C4×C13C25190yes—
55C2×C4×C13C251240yes—
56C2×C4×C13C251720yes—
57#585C22×C1311024yesdirect product factor
58C2×2−1+4C22×C131288yescomplemented
59C2×H(5,𝔽2)C22×C131480yescomplemented
60C22×#41C22×C13120yescomplemented
61C22×#41C22×C13160yescomplemented
62C22×#41C22×C131720yescomplemented
63C23×Q8C22×C13115yescomplemented
64C23×D4C22×C13145yescomplemented
65C24×C4C22×C13115yescomplemented
66C22×C13—2180no—
67C22×C13—4240no—
68C22×C13#58514yesdirect product factor
69C22×C13C26160yes—
70C22×C13C2613yes—
71C4×C13C2614yes—
72C4×C13C26160yes—
73C25C23×C13115yes—
742−1+4C23×C1311536yescomplemented
75H(5,𝔽2)C23×C1312560yescomplemented
76C2×#41C23×C131480yescomplemented
77C2×#41C23×C1311440yescomplemented
78C2×#41C23×C1313840yescomplemented
79C22×Q8C23×C13120yes—
80C22×Q8C23×C131360yescomplemented
81C22×D4C23×C13160yes—
82C22×D4C23×C1311080yescomplemented
83C23×C4C23×C13115yes—
84C23×C4C23×C13145yes—
85C23×C4C23×C131360yescomplemented
86C2×C13—260no—
87C2×C13C2×#58516yesdirect product factor
88C2×C13C2711yescharacteristic
89C24—460no—
90C24C24×C13115yes—
91C24C24×C131180yes—
92#41C24×C1311280yescomplemented
93#41C24×C1313840yescomplemented
94C2×Q8C24×C131240yes—
95C2×Q8C24×C131960yescomplemented
96C2×D4C24×C131720yes—
97C2×D4C24×C1312880yescomplemented
98C22×C4C24×C1311yescharacteristic
99C22×C4C24×C13115yes—
100C22×C4C24×C131180yes—
101C22×C4C24×C131540yes—
102C22×C4C24×C131960yescomplemented
103C13C22×#58511yescharacteristic, direct product factor, Sylow
104C23—260no—
105C23—4360no—
106C23C25×C13190yes—
107C23C25×C131240yes—
108C23C25×C1311yescharacteristic
109Q8C25×C131320yes—
110D4C25×C131960yes—
111C2×C4C25×C1316yes—
112C2×C4C25×C13190yes—
113C2×C4C25×C131240yes—
114C2×C4C25×C131720yes—
115C22—2180no—
116C22—4240no—
117C22C13×#58514yesdirect product factor
118C22C26×C13160yes—
119C22C26×C1313yes—
120C4C26×C1314yes—
121C4C26×C13160yes—
122C2—260no—
123C2C2×C13×#58516yesdirect product factor
124C2C27×C1311yescharacteristic
subgroupG/H
centerC22×C4×C13C24
commutator, Frattini, cosocleC2C27×C13
socleC23×C13C25
LCSG ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C13 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×C13×#585C2direct (N × H)
2. C22×C13×2−1+4C2semidirect
3. C22×C13×H(5,𝔽2)C2semidirect
4. C23×C13×#41C2semidirect
5. C13×#585C22direct (N × H)
6. C2×C13×2−1+4C22semidirect
7. C2×C13×H(5,𝔽2)C22semidirect
8. C22×C13×#41C22semidirect
9. C22×C13×#41C22semidirect
10. C22×C13×#41C22semidirect
11. C23×Q8×C13C22semidirect
12. C23×D4×C13C22semidirect
13. C24×C4×C13C22semidirect
15. C13×2−1+4C23semidirect
16. C13×H(5,𝔽2)C23semidirect
17. C2×C13×#41C23semidirect
18. C2×C13×#41C23semidirect
19. C2×C13×#41C23semidirect
21. C22×Q8×C13C23semidirect
23. C22×D4×C13C23semidirect
26. C23×C4×C13C23semidirect
27. C22×#585C13direct (N × H)
31. C13×#41C24semidirect
32. C13×#41C24semidirect
34. C2×Q8×C13C24semidirect
36. C2×D4×C13C24semidirect
41. C22×C4×C13C24semidirect
42. C2×#585C2×C13direct (N × H)
43. C22×2−1+4C2×C13semidirect
44. C22×H(5,𝔽2)C2×C13semidirect
45. C23×#41C2×C13semidirect
57. #585C22×C13direct (N × H)
58. C2×2−1+4C22×C13semidirect
59. C2×H(5,𝔽2)C22×C13semidirect
60. C22×#41C22×C13semidirect
61. C22×#41C22×C13semidirect
62. C22×#41C22×C13semidirect
63. C23×Q8C22×C13semidirect
64. C23×D4C22×C13semidirect
65. C24×C4C22×C13semidirect
68. C22×C13#585direct (N × H)
74. 2−1+4C23×C13semidirect
75. H(5,𝔽2)C23×C13semidirect
76. C2×#41C23×C13semidirect
77. C2×#41C23×C13semidirect
78. C2×#41C23×C13semidirect
80. C22×Q8C23×C13semidirect
82. C22×D4C23×C13semidirect
85. C23×C4C23×C13semidirect
87. C2×C13C2×#585direct (N × H)
92. #41C24×C13semidirect
93. #41C24×C13semidirect
95. C2×Q8C24×C13semidirect
97. C2×D4C24×C13semidirect
102. C22×C4C24×C13semidirect
103. C13C22×#585direct (N × H)
117. C22C13×#585direct (N × H)
123. C2C2×C13×#585direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C13×#5852
C22×C13×2−1+42
C22×C13×H(5,𝔽2)2
C23×C13×#412
C22×#58513